High-Throughput Survey of Ordering Configurations in MXene Alloys Across Compositions and Temperatures

2D transition metal carbides and nitrides known as MXenes are gaining increasing attention. About 20 of them have been synthesized (more predicted) and their applications in fields ranging from energy storage and electromagnetic shielding to medicine are being explored. To facilitate the search for double-transition-metal MXenes, we explore the structure-stability relationship for 8 MXene alloy systems, namely, (V_1-xMo_x)₃C₂, (Nb_1-xMo_x)₃C₂, (Ta_1-xMo_x)₃C₂, (Ti_1-xMo_x)₃C₂, (Ti_1-xNb_x)₃C₂, (Ti_1-xTa_x)₃C₂, (Ti_1-xV_x)₃C₂, and (Nb_1-xV_x)₃C_2, with 0 ≤ x ≤ 1, using high-throughput computations. Starting from density-functional theory calculated formation energies, we used the cluster expansion method to build quick-to-compute interactions, enabling us to scan through the formation energies of millions of alloying configurations. For the Mo-rich MXenes, (M1_1-xMo_x)₃C₂ (where M1: Ti, V, Nb, Ta) Mo atoms prefer to occupy the surface layers, and ordering persists to high temperatures, based on our Monte Carlo simulations. When Ti is alloyed with Nb or Ta, in the Ti-rich MXenes, Ti atoms prefer the surface layers (e.g., Ti-C-Nb-C-Ti sequence), and in the Nb- or Ta-rich MXenes, Ti occupies only one surface layer and the other two layers are Nb or Ta (e.g., Ti-C-Nb-C-Nb), exhibiting asymmetric ordering. However, alloying Ti with V results in solid solutions across all compositions. (Nb_1-xV_x)₃C₂ phase separates at lower temperatures but forms solid solutions at synthesis temperatures. Postsynthesis annealing at moderate temperatures (800 to 1000 K) increases the ordering for all the compositions. Lastly, by investigating the stability of their precursor MAX phases and surface-terminated MXenes, we discuss the synthesis possibilities of highly ordered MXenes.